Abstract
For a certain class of partial differential equations in cylindrical domains, we show that all small time-dependent solutions are described by a reduced system of equations on the real line, which contains nonlocal terms. As an application, we investigate the system describing nonlinear water waves travelling on the free surface of an inviscid fluid. Two-dimensional gravity waves are characterized by the parameter λ , the inverse square of the Froude number. For λ close to the critical value λ0=1 , we obtain a reduced system of four nonlocal equations. We show that the terms of lowest order in μ=λ-1 lead to the Korteweg—de Vries equation for the lowest-order approximation of the free surface.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
